Lobed composite flexbeam

ABSTRACT

The lag-torsion flexure portion (16) of a flexbeam (10) having segregated lag-torsion flexure portions (16) and flap flexure portions has multiple longitudinal lobes (98A-98G, 100A-100G) formed by multiple grooves (90A-90F, 92A-92F) extending from the upper (94) and lower (96) surfaces of the lag-torsion flexure portion to a central planar portion (102) thereof. The bases of the grooves are radiused (r) for favorable stress distribution while allowing for torsional and lead/lag softness in the lag-torsion flexure portion. The preferred number of grooves is an even number, such as six, resulting in an odd number of lobes. The lobes may decrease in height from the central lobe to the edgemost lobes (FIG. 12A). The lobes may be radiused at the upper and lower surfaces of the lag-torsion flexure portions (FIG. 12B). The lobes may be formed of alternate layers of unidirectional longitudinal fiber (32) extending the length of the flexbeam and elastomeric material (112) (FIG. 12D). Furthermore, the central planar portion (102) of the lag-torsion flexure portion may include layers (110) of fibers laid up at an angle to the unidirectional longitudinal fibers (FIG. 12C).

CROSS REFERENCE TO RELATED APPLICATIONS

Cross reference is made to copending, commonly-owned U.S. patentapplication Ser. No. 888,611, July 23, 1986, filed on even date herewithand entitled EXTERNAL WRAP OF COMPOSITE FLEXBEAM.

DESCRIPTION

1. Technical Field

The invention relates to helicopter rotor design and, more particularly,to flexbeams.

2. Background Art

The structural simplicity of a helicopter rotor that allows thecentrifugal loads, as well as all flapping, lead-lag, and torsionalmotions, to be carried by flexible structural elements (flexbeams)rather than by rolling-element or elastomeric bearings is attractive tothe rotor designer. The development of composite materials in recentyears has provided the necessary conditions for the design of rotorswithout bearings, but the apparent structural simplicity of abearingless rotor conceals a number of difficult design problems,including the strain in a flex beam element caused by combineddeformations, aeromechanical stability, blade-pitch control, andredundant structural load paths.

The bearingless-rotor development efforts to date have been successfulin demonstrating that the critical design problems with bearinglessrotors can be overcome. However, with each of these development efforts,success in solving a particular design problem has usually been achievedat the expense of another design goal. For example, long fatigue lifemay be achieved but only by compromising the desired hub-momentstiffness goals.

Flexbeam Design Considerations

A certain minimum cross section is required for a flexbeam to supportblade centrifugal loads. Under normal operating conditions, flapwiseblade deformations will require additional material in the flexbeam todistribute the bending strains, and this increases stiffness and causesthe equivalent flap hinge to move outboard. The lead-lag (chordwise)flexbeam stiffness will be governed by the need to place the rotorlead-lag frequency at about 0.7/rev. If the flexbeam is too soft inchordwise flexibility, the rotor will be more susceptible toaeromechanical instability; if it is too stiff, the chordwise loads willincrease because of dynamic amplification caused by 1/rev resonance. Fortorsional motions, it is necessary to minimize the torsional stiffnessso as not to increase control actuator loads over current designs.

Depending on the details of the flexbeam design, critical loadingconditions may be due to low-cycle/high-strain loading, orhigh-cycle/low-strain loading. In the former case, the flapping andlead-lag loads that occur during startup and shutdown conditions maydictate flexbeam size. As hub-moment stiffness is reduced to meet thetechnical goal, the ability of the flexbeam to carry the static drooploads is decreased until the droop-load condition becomes critical insizing the flexbeam.

High-cycle/low-strain loading will occur because of 1/rev oscillatoryflap, chordwise, and torsional loads in forward flight. The cyclictorsional moments required to control the rotor in forward flightrequire twisting of the flexbeam on the order of ±30°, and thisis also acritical high-cycle/low-strain loading.

Cross-Sectional Tailoring of a Flexbeam

For a flexbeam of uniform cross section, the peak flapping strain willbe at the root end of the flexbeam, and the chordwise and torsionstrains will be relatively constant along the length of the flexbeam. Bytailoring the cross section of the flexbeam along its length, it ispossible to separate the maximum strains into a flapping flexure inboardand a lag-torsion flexure outboard. This has the advantage ofsimplifying the flexbeam design in that the flap and lag-torsionflexures may be individually sized for separate load criteria and forreducing the hub-moment stiffness. The disadvantages of tailored crosssection flexbeams are that they may be difficult to manufacture andthere may be structural difficulties where one cross section transitionsto another.

One approach that tailors the cross section of the flexbeam is the BellHelicopter Model 680. The inboard (flapping flexure) section isrectangular in cross section so that it is relatively stiff chordwiseand in torsion, but soft in flapping. The outer (lag-torsion flexure)section transitions to a triple-H cross section which is stiff flapwise,but relatively soft in lead-lag and torsion.

Lag-Torsion Flexure Deformation Requirements

The lag-torsion flexure is designed both for lead-lag frequencyplacement and to minimize the torsion moment caused by blade twist and,hence, control loads. Within the flexbeam, the moment caused by twistdepends on the shear rigidity, GK, where G is the material shear modulusand K is the cross-sectional inertia term; on cross section warping anddifferential bending effects; and on centrifugal stiffening effects thatdepend on the cross section radius of gyration. The ratio of the shearmodulus to the bending modulus for unidirectional composites issignificantly lower than for isotropic materials, and this provides thedesigner with more flexibility. But despite these material advantages,the cross section must be carefully selected to reduce the twistingmoment.

Pitch-Control Concepts

A pitch-control or torque structure of some kind is required to twistthe blade outboard of the flexbeam to establish the blade collective andcyclic pitch angles. Whether this is a cantilevered pitch horn, a pitchcuff that encloses the flexbeam, or a torque tube that does not enclosethe flexbeam, the primary purpose of the torque structure is to transmita torsional moment to the blade root. Conceptually, the simplestpossible torque structure is a pitch horn extending from the blade rootto the pitch link which is very stiff in bending. In this case, acontrol input will twist the flexbeam, but will also cause a flapdeflection (pitch/flap coupling). The only way in which a pure torsionalmoment can be transmitted to the blade root is if the pitch link load isreacted at the root of the torque structure with a shear restraint. Oncea shear restraint is used at the torque structure root, a number ofadditional design options are opened. The torque structure itself nolonger has to be stiff in flapping and chord, for it need only transmitthe torsion moment.

Materials for Bearingless Hub Designs

The three major composite formulations now used in the helicopterindustry are made of fibers of graphite, fiberglass, or KEVLAR® in anepoxy matrix. The low density and high allowable strain of KEVLAR makeit a very attractive material; however, its very low compressivestrength, approximately 20% of its tensile strength, makes it difficultto use in bearingless hub designs. Graphite-epoxy composites have highstiffness-to-weight ratios and good strain allowables, but relativelypoor fracture toughness. Fiberglass, on the other hand, shows goodstrain allowables and good failure modes, but low stiffness-to-weightratios.

Hub/Flexbeam Attachments

The hub and flexbeam attachment joint is a difficult and importantdesign issue in a number of respects. Blade flapping and chordwisemoments are maximum at the hub center and these loads must betransferred from the flexbeam to the hub and rotor shaft. To minimizehub-moment stiffness, it is necessary to have the flexible portion ofthe flexbeam as close to the center of the hub as possible, and thisminimizes the space available for transferring the high bending loads.It is also desirable to keep the hub small in order to minimize weightand hub drag.

For a four-bladed rotor system one design approach is to clamp twostacked flexbeams perpendicular to one another within a central hub. Ingeneral, unidirectional fibers in each flexbeam connect opposite bladepairs across the hub and hub clamping plates are bolted around theflexbeams; however, the rotor hub moment must be transferred to the hubclamping plates without causing interlaminar shear failures in theflexbeams.

DISCLOSURE OF THE INVENTION

It is an object of this invention to improve the strength of a crossbeamrotor flexbeam without reconfiguring its basic geometry.

According to the invention, the lag-torsion flexure portion of aflexbeam having segregated lag-torsion flexure portions and flap flexureportions has multiple longitudinal lobes formed by multiple groovesextending from the upper and lower surfaces of the lag-torison flexureportion to a central planar portion thereof. The bases of the groovesare radiused for a favorable stress distribution while allowing fortorsional and lead/lag softness in the lag-torsion flexure portion.

The preferred number of grooves is an even number, such as six,resulting in an odd number of lobes. The lobes may decrease in heightfrom the central lobe to the edgemost lobes (FIG. 12A). The lobes may beradiused at the upper and lower surfaces of the lag-torsion flexureportions (FIG. 12B). The lobes may be formed of alternate layers ofunidirectional longitudinal fibers extending the length of the flexbeamand elastomeric material (FIG. 12D). Furthermore, the central planarportion of the lag-torsion flexure portion may include layers of fiberslaid up at an angle to the unidirectional longitudinal fibers (FIG.12C).

Other objects, features and advantages of the invention will become moreapparent in light of the following description thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of the flexbeam of this invention.

FIG. 2 is a perspective view of two flexbeams according to FIG. 1.

FIG. 3 is a cross-sectional view of the flap flexure portion of theflexbeam of FIG. 1, taken along the section 3--3.

FIG. 4 is a graph showing characteristics of the flap-flexure portion ofthe flexbeam of this invention.

FIG. 5 is a graph showing characteristics of the flap-flexure portion ofthe flexbeam of this invention.

FIG. 6 is a graph showing characteristics of the flap-flexure portion ofthe flexbeam of this invention.

FIG. 7 is a graph showing characteristics of the flap-flexure portion ofthe flexbeam of this invention.

FIG. 8 is a table showing characteristics of the flap-flexure portion ofthe flexbeam of this invention.

FIG. 9 is a graph of twist angle (out of a plane normal to therotorshaft axis) versus position (expressed in % rotor radius) for theflexbeam of this invention and a typical blade.

FIG. 10 is a cross-sectional outline of the lag-torsion portion of theflexbeam of this invention taken along 10--10 of FIG. 2.

FIG. 11 is a cross-sectional outline of the flexbeam of this inventiontaken along line 11--11 of FIG. 2.

FIG. 12A is a cross-sectional outline of an alternate embodiment of thelag-torsion flexure portion of the flexbeam of this invention.

FIG. 12B is a cross-sectional outline of an alternate embodiment of thelag-torsion flexure portion of the flexbeam of this invention.

FIG. 12C is a cross-sectional outline of an alternate embodiment of thelag-torsion flexure portion of the flexbeam of this invention.

FIG. 12D is a cross-sectional outline of an alternate embodiment of thelag-torsion flexure portion of the flexbeam of this invention.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 shows the flexbeam 10 of this invention. The flexbeam isessentially symmetric about the rotorshaft axis 11 and comprises thefollowing major portions; a hub portion 12 attaching to the rotorshaft,an inboard flap flexure portion 14, an outboard lag-torsion flexureportion 16, and a blade-attachment portion 18 at the extreme outboardend of the flexbeam. The entire flexbeam 10 is preferably a unitarycomposite structure suitable for attaching two blades (not shown) to therotorshaft and allowing the previously discussed requisite degrees ofblade freedom. For a four-bladed rotor system, two such flexbeams wouldbe overlapped at 90°, as shown in FIG. 2, their hub portions 12overlapping at the axis 11 of the rotorshaft 20 and clamped thereto viaan upper hub plate 22 and a lower hub plate 24, as shown. It will benoted that the pair of blades associated with one flexbeam will beslightly out of plane with respect to the pair of blades associated withthe other flexbeam with this arrangement, but it has been determinedthat this condition is entirely acceptable. Else, the hub portions ofone or both flexbeams would need to be "stepped" to bring the two pairsof blades into a single plane. This would add unwarranted complexity tothe flexbeam design.

The flexbeam is essentially symmetric with respect to the rotorshaftaxis. In that the flexbeam is required to react centrifugal blade loads,it is largely made up of composite fibers (or rovings), such as KEVLAR®,E-glass, or graphite which are laid up unidirectionally along the length(longitude) of the flexbeam (i.e., radial to the rotorshaft axis). Onespecific suitable composite fibre is CELION ST® (available from CelionCorp.), bound in a toughened matrix of 6376 epoxy resin (available fromCiba-Geigy).

The hub portion 12 of the flexbeam is rectangular in cross section(normal to the flexbeam length), made up of several layers (or plies) ofthe aforementioned composite fibers, said layers definingvertically-stacked planes normal to the rotorshaft axis 11. Anelliptical hole 25 is disposed through the hub portion at the rotorshaftaxis, the major axis of the ellipse being aligned longitudinally withrespect to the flexbeam (as best viewed in FIG. 1). An elliptical holeso aligned will minimize the stress concentration factor across theflexbeam, a concept which is disclosed in greater detail incommonly-owned U.S. Pat. No. 4,008,980 (Noehren, et al., 1977).

The blade-attachment portion 18 of the flexbeam is strengthened withcross plys (layers of fibers at 45° to the flexbeam length in planesnormal to the rotorshaft axis) to permit drilling of suitablydimensioned holes 26 to receive the blade root via two bolts (not shown)disposed nearly parallel to the rotorshaft (not quite parallel theretodue to preconing in the flexbeam).

Torque tubes 28 are shown (in phantom) extending from a pitch horn 29 atan inboard location on the flexbeam to the outboard blade attachmentportion 18.

Flap Flexure Portion

The flap flexure portion 14 of the flexbeam is rectangular in crosssection (normal to the flexbeam length), tapering in width from agreater width at its inboard end where it meets the hub portion 12 to alesser width at its outboard extreme where it meets the lag-torsionflexure portion 16, and tapering in thickness from a greater thicknessat its inboard extreme to a lesser thickness its outboard extreme tomatch the thicknesses of the hub and lag-torsion flexure portions,respectively. The relative length of the flap flexure portion isapproximately 10% of the overall rotor radius (rotorshaft axis to bladetip).

Referring to FIG. 3, which is a cross section of the flap flexureportion 14, the flap flexure portion has a rectangular core 30 made upof several vertically-stacked layers (plies) 31 of the aforementionedcomposite fibers 32.

Extensive fatigue testing of several main and tail rotor flexbeamdesigns has shown that the structural performance of the flexbeam islimited by interlaminar cracks that occur between the plies 31 of thecomposite material. During testing, cracks originate at the edge of theflexbeam and propagate inward causing a loss of stiffness and strength.Although not catastropic, this failure mode limits the service life ofthe flexbeam.

A careful study of these interlaminar cracks revealed that they werecaused by a combination of loadings and stress concentration that causedlocalized interlaminar shear stress peaks to occur along the edge of theflexbeam. It was determined that a selectively tailored overwrap couldreduce these interlaminar shear stresses in the flap flexure regionwithout compromising any of the other attributes of the flexbeam.

Therefore, as seen in FIGS. 1 and 3, the core 30 of the flap flexureportion 14 is covered by an external wrap 34 made up of composite fibers36 having an angular orientation with respect to the longitudinal corefibers 32. The orientation of the external wrap fibers 36 is preferably±45° with respect to the core fibers 32.

The external wrap 34 has a significant effect on reducing each of thefollowing four factors that contribute to interlaminar shear stresses inthe layers 31 of the core. As stated, interlaminar shear stresses arethe primary factor limiting the life of the flap flexure portion. Thefour factors are:

1.Imposed pitch (torsion) forces;

2.Ply endings in the core section; and

3.Flatwise shear forces;

4.Twisting moments induced by bending deflections multiplied by shearforces.

The external wrap reduces the shear stress factors (1 and 4) by locallyincreasing the torsional rigidity due to the shear modulus of the angleplies (external wrap fibers 36).

The second factor, ply endings in the core section, produced by thetransfer of axial and bending stresses around ply endings is reduced bythe local increase in bending stiffness of the wrap term. The thirdfactor, based on Lekhnityskii's equation for wide anistropic beams, isalso reduced by the local increase in flapwise bending and shearstiffness.

The effects of each term (factors 1-4) can be tailored by proper choiceof wrap material, thickness, and angle orientation; and is well withinthe purview of one skilled in the art.

The graphs of FIGS. 4-6 plot for different composite fibers the expectedeffect of the external wrap on the shear stresses under maximum flightloads. The graph of FIG. 7 plots bending strain allowables to a ±45°external wrap.

The graph of FIG. 4 is a plot of vibratory shear stress (vertical axis)versus position (horizontal axis) along the flexbeam (in the flapflexure portion only) from "inboard" (towards the rotorshaft) to"outboard" (towards the blade). The curve 40 represents the stress in anunwrapped flap-flexure portion, the curve 42 represents the stress in aflap-flexure portion having a 0.050" thick external wrap of ±45° E-glass(about 5 plies), and the curve 44 represents the stress in aflap-flexure portion having a 0.100" thick external wrap of ±45°E-glass. One will readily appreciate the reduction in vibratory shearstress attributable to the external wrap.

The graph of FIG. 5 is a plot of vibratory shear stress versus flexbeamlongitudinal position (station) similar to FIG. 4 for an unwrapped 50,0.050" wrapped 52, and a 0.100" wrapped 54 flap-flexure portion. In thiscase, the external wrap is ±45° graphite fibers.

Likewise, the graph of FIG. 6 shows curves for an unwrapped 60, 0.050"wrapped 62, and a 0.100 wrapped 64 flap flexure portion, using ±45°KEVLAR fiber in the external wrap.

If the graphs of FIGS. 4-6 were overlapped, one would notice that thegraphite external wrap (FIG. 5) results in the greatest reduction invibration shear stress in the flap flexure portion, E-glass (FIG. 4)results in a slightly lesser reduction, and Kevlar (FIG. 6) results inthe lowest reduction.

The graph of FIG. 7 is a plot of maximum vibratory bending strain in theflap flexure portion (vertical axis) versus wrap thickness (horizontalaxis) showing curves 70,72,74 for ±45° external wrap of E-glass,graphite, and KEVLAR, respectively. From this graph it is apparent thatgraphite fibres are the best choice of composite material for theexternal wrap of the flap flexure portion, since the strain is both lessthan and decreases more dramatically than that of KEVLAR or E-glass.(Actually, the strain in the KEVLAR was found to increase withthickness.)

The table of FIG. 8 presents a tabulation of K.sub.θ (torsionalstiffness), T₁ /θ (maximum shear stress at the midpoint of the flapflexure edge), and G_(wrap) (shear modulus of the wrap itself) for anunwrapped flap flexure, and flap flexures externally wrapped with ±45°E-glass, KEVLAR, and graphite of 0.050" and 0.100" thickness,respectively. The table indicates that the torsional stiffness of theflap flexure portion increases when the external wrap is appliedthereto; graphite exhibiting the greatest increase in torsionalstiffness over an unwrapped flap flexure.

An advantage of the external wrap is that the service life of flexbeamsin use can be extended by the addition of the external wrap. Thisimplies that new tooling would not be required for fabrication of the"basic" (unwrapped) flexbeam.

The external wrap can be filament wound, or applied by hand. Theexternal wrap can be an add-on to existing flexbeams, or can be integralwith a new design flexbeam.

The external wrap extends the life of (otherwise) limited-lifeflexbeams, and allows local changes to flexbeam properties withoutsignificantly affecting overall flexbeam features. The invention isapplicable to main or tail rotors and should result in a 30-35% increasein fatigue strength over current technology flexbeam designs.

Dynamic modeling of the flap flexure portion of the flexbeam of thisinvention has exhibited fatigue endurance of seven degrees of flappingfreedom According to published data, Bell Helicopter's Model 680flexbeam exhibits only 3-4 degrees of flap per se, additional flappingfreedom being contributed by a long flexible rotorshaft. A longrotorshaft is undesirable.

It is known to provide a blade with built-in negative twist for enhancedhover performance. Therefore, the flexbeam 10 may be provided with abuilt-in positive twist so that there is no net twist at the hub. Thismay be accomplished either by twisting the flap flexure portion 14out-of-plane with respect to the hub portion 12 at the junction thereof(e.g., ten degrees), or by twisting the blade attachment portion 18out-of-plane with respect to the lag-torsion flexure portion 16 at thejunction thereof (e.g., four degrees), or a combination of both. Ofcourse, twisting the flap flexure portion out-of-plane would soften itsedgewise stiffness (lower W_(E)). The preferable edgewise stiffness forthe flap flexure portion is 0.70 per rev. W_(E). The built-in twist ofthe flexbeam is not evident in FIGS. 1 and 2.

To enhance hover performance it is also desirable that the outboard endof the torque tube (28) be at the same aerodynamic angle of attack asthe blade root, and to minimize profile drag it is desirable that theinboard end of the torque tube be feathered. Also, it has been foundthat a positive twist in the flap flexure portion of the flexbeamimproves aeroelastic stability through favorable flap/lag couplings. Theoptimum combination of flexbeam and torque tube twist which producesgood aerodyanmic performance and enhanced stability is shown in FIG. 9.Note that the flexbeams are not twisted in their hub portion (12)because to do so would increase the separation between the upper andlower flexbeams where they pass in close proximity to each other.

FIG. 10 shows the lag-torsion flexure portion 16 pretwisted with respectto the flap flexure portion 14.

It is also desirable to provide a measure of preconing in the flexbeamto reduce flexbeam flapwise strains caused by rotor thrust. Thus, theflap flexure portion 14 is tilted upwards out-of-plane with respect tothe hub portion 12 at the junction thereof. The desired amount ofpreconing is a function of helicopter gross weight.

Lag-Torsion Flexure Portion

When torsional forces (pitch control inputs and/or aerodynamic forces)are applied to the blade root end (i.e., the blade-attachment portion 18of the flexbeam), it is intended that the lag-torsion flexure portion 16of the flexbeam twist in response thereto, and that the flap flexureportion 14 does not. It is also desirable that the lag-torsion flexureportion be somewhat flexible in-plane (low W_(E)) so that blade lead/lagactivity is accommodated in this portion of the flexbeam. Lastly, it isof utmost importance that the lag-torsion flexure portion of theflexbeam be extremely stiff in the flapwise (vertical) direction (highW_(F)) so that the effective hinge offset is concentrated in the inboardflap flexure portion of the flexbeam. Effective hinge offset isdiscussed in detail in commonly-owned U.S. Pat. No. 4,323,332(Fradenburgh, 1982).

A multiple-lobed H-beam (crossbar of the H's in-plane, uprights of theH's vertically-aligned) fits the bill quite nicely for achieving thesedesign objectives. The Bell Helicopter Model 680 triple-H (threegrooves, four lobes) lag-torsion flexure portion cross section is noted.Therein, the grooves and lobes H's are essentially square in crosssection.

As is readily observable in FIG. 2, the lag-torsion flexure portion 16of the flexbeam 10 is multiple-lobed, and hence, multiple-grooved. Thelobed lag-torsion flexure portion 16 provides a structural solution fora soft in-plane rotor system while still maintaining the dynamicrequirements, i.e., simultaneously,

a. to provide a high section modulus in the chordwise direction (toachieve acceptable strain levels for coriolis generated edgewisemoments);

b. to maintain an acceptable chordwise moment of inertia (to achieveacceptable dynamic response);

c. to minimize torsional stiffness (to achieve acceptable control loadsand shear stresses due to feathering);

d. to minimize torsional shear stresses and;

e. to maintain an acceptable twist-bend buckling strength.

FIG. 11 is a cross-sectional outline of the lag-torsion flexure portion16 of the flexbeam 10. One can envision six longitudinal slots (grooves)90A-90F, 92A-92F being machined in both the upper 94 and lower 96surfaces of an otherwise rectangular (cross section) member, resultingin seven flanges 98A-98G, 100A-100G. The grooves extend from the upperand lower surfaces 94, 96 of the member a depth t' approximatelyone-third of the overall thickness T through the member to a centralplanar (in-plane with respect to the flexbeam and midway between itsupper and lower surfaces) portion 102 of thickness t, as shown. Thegrooves are radiused (r) at their bases, which is defined as the portionof the grooves adjacent the central planar portion 102. A centerline 104for the flexbeam is defined as a middle position on the flexbeam withrespect to its width (b).

It is of no little consequence that an even number of grooves (resultingin an odd number of lobes) was chosen for this design, and that thecentral lobes 98D,100D are disposed on the centerline 104 of theflexbeam. Looking at the effects resulting from torsional forces appliedaround the centerline to a multiple-lobed beam projecting from a wall,by having a lobe at the centerline more of the cross-sectional materialis at the centerline, which in this case is the feathering axis. Hence,the beam is more torsionally soft. (The Bell 680 has an even number oflobes.)

The geometry of the lobed section is determined from the followingseries of closed form equations which for given flexbeam designreguirements can tailor an efficient lag-torsion flexure portion.

A. Torsional Stiffness (J) ##EQU1##

B. Chordwise Moment of Intertia (I_(C)) ##EQU2##

C. Flatwise Moment of Intertia (I_(F)) ##EQU3##

D. Applied Strain (E) ##EQU4## wherein: b is the section width;

t is the central thickness (see FIG. 11);

N is the number of lobes;

b is the lobe width;

t is the groove depth;

d is the distance between lobes;

T is the total thickness of the lobes;

M_(C) is the chordwise moment; and

M_(F) is the flatwise moment.

These first four equations A-D were applied to a model of thelag-torsion flexure portion that had squared lobes (as in the Bell 680),since the lobe radii are somewhat irrelevant to these parameters(torsional stiffness, moment of inertia for flatwise/edgewise bending).The equations A-D verify that buckling and axial strains are satisfiedfor the present design.

Equations E-H are derived from Timoshenko's equations (Strength ofMaterials, 3rd Edition) for filleting (radiusing) in shafts and verifythat radiusing the lobes satisfies torsional shear stress (from appliedtorque) criteria. The radius r (for the cross section shown in FIG. 11)is determined by the following equations E-H.

E. Applied Torque ##EQU5##

F. Torsional Shear Stress (S) ##EQU6##

G. Torsional Stress Concentration (K_(T)) ##EQU7##

H. Twist-Bend Buckling Strength (M_(CR)) ##EQU8## wherein: G is theshear modulus;

J is the torsional stiffness;

θ is the twist angle;

L is the length of the lobed section;

P is pi;

T_(C) is the centrifugal force; and

K is the radius of gyration.

The resulting cross section of the lag-torsion flexure portion satisfiesall of the structural and dynamic requirements of a soft in-planebearingless rotor, and is not gust sensitive. The gust sensitivity of ahingeless rotor is discussed in an article by Bir and Chopra (Journal ofthe American Helicopter Society, Vol. 31, No. 2, page 33, April 1986).

It should be noted that the large number of lobes and full radius at thebottom of each groove provides increased torsional performance relativeto the prior art (Bell 680) which has no groove blend radius (r) andtherefore a high torsional stress concentration factor.

The applied torque is resolvable into two components; pure torsion anddifferential bending. The latter has been discussed with respect to thelobes, and it is predictable that the highest shear load will be in theoutermost (98A,100A and 98G,100G) lobes. Thus, FIG. 12A represents across section for the torsion flexure specifically tailored to equalizeshear stresses in the flanges (the height t' of the flanges decreasesfrom the centermost flanges 98D,100D, (the flanges immediately on thelongitudinal centerline 104 of the flexbeam) to the edgemost lobes98A,98G,100A,100G (the lobes at the leading/trailing edges of theflexbeam).

Conceivably, one could tailor the radius (r) of each groove to optimizethe torsion flexure characteristics. However, insofar as pure torsion(resulting from applied torque) is concerned, this would have nosignificant effect. Furthermore, in the case of machined-out grooves, amultiplicity of tools would be required. Nevertheless, if the lobes wereformed in a molding process, r could be tailored on a groove-by-groovebasis.

Molding the lobes, or a combination of molding and machining isprojected as the preferred process for achieving the torsion flexurelongitudinal cross sections shown in FIGS. 12B and 12C. In FIG. 12B thelobes are radiused at the upper and lower surfaces of the lag-torsionflexure to provide a modified stiffness distribution.

FIG. 12C shows a layer 110 (or layers) of composite material disposed atthe midplane of the lag-torsion flexure portion and laid up at an angle,such as ±45° to the longitudinal fibers. (The midplane is the centralregion of the lag-torsion flexure midway between the upper and lowersurfaces thereof and is within the central planar portion 102--see FIG.11.) This embodiment would have the advantage of enhanced in-plane shearstrength without an increase in torsional stiffness.

FIG. 12D shows an embodiment of the lag-torsion flexure portion whereinthe flanges incorporate alternating layers of elastomer 112 andcomposite fibers 114 (32). This embodiment would have the advantage ofreduced torsional stiffness and stresses.

SUMMARY

This invention is accomplished while maintaining minimum flexbeam weightand is within the state of the art fiber matrix manufacturingtechnologies.

1. The flexbeam 10 segregates the flap and lag-torsion flexure regionsto improve fatigue performance.

2. The flap flexure portion is wrapped with a ±45° filament winding toreduce interlaminar shear stresses and to force all torsionaldeflections to occur in the lag-torsion flexure portion. Since the flapflexure portion does not have to twist it can accommodate higherflapping motion.

3. The lag-torsion flexure portion begins outboard of the flap flexureportion (a unique point as defined from the blade mode shape) so as tonot increase the rotor hub moment stiffness. High hub moment stiffnesscauses vibration and large rotor shaft fatigue stresses. An 8%equivalent hub moment offset has been demonstrated with the flexbeam 10.

4. The lobed cross section shape of the lag-torsion flexure portion isoptimized to produce the best balance of stiffnesses, torsionalstresses, and bending stresses. Seven lobes with a full radius grooveappear to be optimum.

5. The flexbeam and torque tube are twisted as in FIGS. 9 and 10 tooptimize aerodynamic performance while providing favorable aeroelasticflap/lag couplings without increasing the separation between the upperand lower flexbeams where they pass within close proximity.

It should be understood that any multiple-lobed lag-torsion flexureportion of a flexbeam could benefit from the teachings illustrated inFIGS. 11 and 12A-12D.

We claim:
 1. A flexbeam (10) having a hub portion (12), a flap flexureportion (14) outboard of the hub portion, a lag-torsion flexure portion(16) outboard of the flap flexure portion, and a blade attachmentportion (18) outboard of the lag-torsion portion, and having fibers (32)of composite material extending longitudinally the length of theflexbeam, characterized by:a plurality of longitudinal lobes (98A-98G,100A-100G) defined by a plurality of radiused grooves (90A-90F, 92A-92F)extending into the lag-torsion flexure portion of the flexbeam from theupper and lower surfaces (94, 96) of the lag-torsion flexure portion toa central planar portion (102) of the lag-torsion flexure portion, thegrooves being radiused at their bases to enhance the torsion flexurecharacteristics of the lag-torsion flexure portion.
 2. A flexbeamaccording to claim 1 characterized in that the grooves are radiusedaccording to the formula: ##EQU9##
 3. A flexbeam according to claim 1characterized in that the number of lobes is odd.
 4. A flexbeamaccording to claim 3 characterized in that the number of lobes is seven.5. A flexbeam (FIG. 12A) according to claim 1, characterized in that:thebases of the grooves from each surface of the lag-torsion flexureportion are coplanar; and the lobes decrease in height from thecentermost lobes (98D, 10D) to the edgemost lobes (98A,100A,98G,100G).6. A flexbeam (12B) according to claim 1 characterized in that theflanges are radiused at the upper and lower surfaces of the lag-torsionflexure portion.
 7. A flexbeam (12C) according to claim 1 characterizedin that at least one cross ply layer of composite material is desposedin the central planar portion of the lag-torsion flexure portion.
 8. Aflexbeam (12D) according to claim 1 characterized in that thelongitudinal fibers (32) are layered in the lag-torsion flexure portionand that layers of elastomer material are interposed between the layersof longitudinal fibers in the lobes.
 9. A flexbeam according to claim 1characterized in that the flexbeam includes at least five lobes.